Radius/interval of convergence

  • Thread starter karadda
  • Start date
  • #1
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Homework Statement




[tex]\Sigma[/tex] n!(2x-1)[tex]^{}n[/tex]

from n=1 to infinity

Homework Equations



-ratio test

The Attempt at a Solution



lim n-> infinity | (n+1)!(2x-1)^(n+1) / n!(2x-1)^n |

lim n-> infinity | (n+1)(2x-1) |

|2x - 1| lim n-> infinity | (n+1) |

-1 < 2x -1 < 1

0 < 2x < 2
0 < x < 1



I know at this point I've done something pretty wrong. as my interval and radius doesnt match up with the back of the book. could use a push in the right direction, thanks.
 

Answers and Replies

  • #2
Dick
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What happened to the lim n->infinity |n+1|? Did you just drop it?
 
  • #3
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oh, im not too sure what to do with it. i understand that the limit goes to infinity, UNLESS x = 1/2 in which case it goes to 0. how do i proceed knowing that?

nm, i should just stop there ;)

1/2 is the only value of x for which this will converge, so the interval of convergence is {1/2}. the radius is 0.
 
Last edited:
  • #4
Dick
Science Advisor
Homework Helper
26,260
619
oh, im not too sure what to do with it. i understand that the limit goes to infinity, UNLESS x = 1/2 in which case it goes to 0. how do i proceed knowing that?

nm, i should just stop there ;)

1/2 is the only value of x for which this will converge, so the interval of convergence is {1/2}. the radius is 0.
I couldn't have said it better myself.
 

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